Estimating Magnetic Field Strength from the. TLRBSE Solar Spectra Data

Transcription

1 Estimating Magnetic Field Strength from the TLRBSE Solar Spectra Data March 2006

2 INTRODUCTON to a SUNSPOT & a COUPLE of SOLAR SPECTRA THE SOLAR SURFACE : PHOTOSPHERE PARTS OF A SUNSPOT: PENUMBRA of SUNSPOT UMBRA of SUNSPOT A sunspot is focused on the slit at the telescope. A telescope mirror is moved in increments so that the slit marches from one side of the sunspot to the other. It may take 200 steps to do so and at each step, a spectrum is taken, creating in all 200 spectra or 200 spectral files, e.g. in directory Apr05_scan06. RESULTING SPECTRUM: THE SLIT 15, Angstroms 15, Angstroms RESULTING SPECTRUM: WAVELENGTH (Angstroms)

3 This is a description of the steps to take to calculate magnetic field strength: With the PLOT button as described in Section of the User s Guide, you can graphically measure quantities from the images. For example, the plot in the figure below can be used to determine the dispersion (the pixel size in units of wavelength) of the spectrum by comparing the plot to a spectral atlas. This plot is a spectrum at the beginning of the march across the sunspot as shown on in the illustration on the previous page. It is the first file under the reduced data (e.g, file olc_act_region_lft_pol.o.i.gdc.001 in the directory Apr05_scan06reduced) and it samples the photosphere whose magnetic fields are too weak to produce any Zeeman-split lines. Placing the cursor at the minimum of the central spectral line (and pressing on the rightmost mouse button) will give the x-coordinate reading similar to pixels as seen in the resulting pop-up window:

4 Placing the cursor at the minimum of the prominent spectral line to the left of center (and pressing on the right-most mouse button) will give the x-coordinate reading similar to pixels. Take the difference of these two x-coordinate values. You will use this difference value shortly. From a page in a solar spectral atlas seen below, pick out the same two lines. If you were able to tell precisely from the spectrum above, the two lines would have wavelengths of Angstroms, the prominent line toward the center of the red box, and Angstroms, the prominent line on the left side of the red box. Take the difference of these two wavelength values. The dispersion is the ratio of the difference in wavelength values to the difference in x- coordinate values of these two spectral lines. Calculate this ratio. It should be close to 0.05 Angstroms/pixel. You need only do this calculation for dispersion once per observing run. Once made, you can use the same dispersion value over and over for different calculations of magnetic field strength.

5 Next on the way to getting a magnetic field strength is the measurement of the Zeeman splitting in a sunspot. Again using the PLOT button, choose a file midway down the list of files in the LCP reduced data file directory, where the splitting in this case will be most pronounced. Or as you saw in the User Guide, Section 4, Step #10 with the MOVIE button, use the frame number (or file) showing the strongest sunspot signature. (In the case of directory Apr05_scan06reduced, this could be the 100 th frame or the file old_act_region_lft_pol.o.i.gdc.100.) Toward the center of the spectrum, you should see the main component of the line plus a component to the right (the LCP component). Choose your ROI just around these components. Using PLOT button as described in Section of the User s Guide, you can read off values in the plot by placing the cursor on the desired point and then pressing the rightmost mouse button. This will pop up a status screen with the x and y coordinates in terms of pixels. Make this measurement for the central and the right components of the prominent line near the middle of the spectrum. What are those x-coordinate pixel values? What is the difference between them? It should be around 13 pixels.

6 Then open the same file in the RCP reduced data file directory (e.g., old_act_region_rt_pol.o.i.gdc.100 in Apr05_scan07reduced). Make the same measurement for the central and left components of the prominent line near the middle of the spectrum. What are those x-coordinate pixel values? What is the difference between them? It should be around 14 pixels. Let s take stock. You got around 13 pixels for the difference between the central and right components and around 14 pixels for the difference between the central and left components of the main spectral line. Average the two results and call it dp short for difference in pixels. You calculated the value for the dispersion to be around 0.05 Angstroms per pixel. How might you use this number for disperson and the value for dp to get the average difference between the central and right or left components of the line in terms of Angstroms instead of pixels? The result should be close to 0.67 Angstroms. Talk about tiny. An Angstrom is meters. That s quite a powerful amount of spectral resolution that the McMath-Pierce Solar Telescope has.

7 Now you have all the ammunition you need to calculate the magnetic field strength. Here is the formula to get the magnetic field strength, B, in units of Gauss: B = 2.13 x [ / ( 2 x g)] where is the average difference between line components in Angstroms OR the measurement of the Zeeman-split which is proportional to the strength of the magnetic field. Here the value was close to 0.67 Angstroms. is the wavelength of the main component of the line you observed the Zeemansplitting. Here the value was 15, Angstroms. g is the Lande g factor, which for this particular Fe I or neutral iron line is 3. See the Glossary of Technical Terms for a definition. Using the numbers that you got, see if you get a value between 1900 and 2000 Gauss for the strength of the magnetic field. CONGRATULATIONS! The calculation for magnetic field strength is made within the software program, TSSDAP, and is part of the process that generates the magnetograms. However, it is good to understand how the software produces the magnetograms by manually going through the calculation for magnetic field strength at least once, as you have done here.